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Articles published week ending22 JUNE 2007

Volume 98, Number 25

Magnetoelectrostatic Trapping of Ground State OH Molecules

Brian C. Sawyer,* Benjamin L. Lev, Eric R. Hudson,† Benjamin K. Stuhl, Manuel Lara, John L. Bohn, and Jun YeJILA, National Institute of Standards and Technology and University of Colorado,

Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA(Received 16 February 2007; published 21 June 2007)

We report magnetic confinement of neutral, ground state OH at a density of �3� 103 cm�3 andtemperature of�30 mK. An adjustable electric field sufficiently large to polarize the OH is superimposedon the trap in various geometries, making an overall potential arising from both Zeeman and Stark effects.An effective molecular Hamiltonian is constructed, with Monte Carlo simulations accurately modeling theobserved single-molecule dynamics in various trap configurations. Magnetic trapping of cold polarmolecules under adjustable electric fields may enable study of low energy dipolar interactions.

DOI: 10.1103/PhysRevLett.98.253002 PACS numbers: 33.80.Ps, 33.15.Kr, 33.55.Be, 39.10.+j

Cold and ultracold molecules are currently subject tointense research efforts as they promise to lead majoradvances in precision measurement, quantum control,and cold chemistry [1]. Much of this interest has focusedon molecules possessing permanent electric dipole mo-ments. The long range, anisotropic dipole-dipole interac-tion leads to novel collision [2,3] and reaction [4]dynamics, and may serve as the interaction between mo-lecular qubits [5] in architectures for quantum informationprocessing [6]. Quantum phase transitions can be exploredwith polar molecules [7]. Furthermore, polar moleculesmay possess extremely large internal electric fields (onthe order of gigavolts per centimeter), yielding dramaticsensitivity enhancement to searches for an electron electricdipole moment [8,9]. Cold polar molecules have beenproduced via photoassociation of ultracold atomic species[10,11], Stark deceleration [12,13], and buffer gas cooling[14].

Polar molecules are readily trapped in inhomogeneouselectric fields [15,16]; however, theory suggests that athigh phase-space densities such traps invariably sufferfrom large inelastic collision losses [17]. One possiblesolution is to trap strong-field seeking states via time-dependent electric traps [18]. In contrast, we are interestedin magnetically trapping these neutral polar molecules soas to have the freedom to apply external electric fields tocontrol collision dynamics inside the trap. Highly vibra-tionally excited, triplet KRb molecules produced via pho-toassociation have been magnetically trapped at atemperature of �300 �K and density of 104 cm�3 [19].Buffer gas cooling has been used to load a magnetic trapwith ground state CaH and NH molecules at temperaturesof hundreds of millidegrees Kelvin and densities of�108 cm�3, but in the presence of a cold He buffer gas[14,20]. We report here the first observation of magneti-cally trapped hydroxyl radical (OH) molecules and thelowest temperature (30 mK) yet achieved for a magneti-cally trapped polar molecule in its rovibronic ground state.Moreover, we perform the first study of trap dynamicsbased on a single molecule possessing large magnetic

and electric dipole moments in magnetic (B) and electric(E) fields that are inhomogeneous and anisotropic. Inter-esting polar molecule dynamics have been predicted atlarge field strengths [21]. Accurate correspondence be-tween experimental data and simulations is achieved onlyby accounting for the molecular state mixing induced bythe crossed fields. Large B fields may serve to suppressinelastic collision losses [22] while at the same time sym-pathetic cooling of molecules via cotrapped ultracoldatoms may become feasible [23]. In addition, the magneticquadrupole trap described here, in contrast to electrostatictraps, permits the application of arbitrary external E fieldsto a large class of polar molecules—a necessary steptowards observing cold molecule dipole-dipole collisions[24].

To magnetically trap OH, we begin with a cold beam ofground state (2�3=2) OH produced via a pulsed electricdischarge through 2% H2O vapor [25] seeded in 1.5 bar ofKr. A piezoelectric transducer valve [26] operating at10 Hz provides a supersonic expansion of the OH=Krmixture through a 1 mm nozzle. This results in a490 m=s molecular packet with a 15% longitudinal (z)velocity spread. The transverse (�) velocity spread of thebeam is limited to 2% by the 3 mm diameter molecularskimmer. Compared with a Xe expansion, the higher-velocity Kr expansion leads to less transverse beam losswithin the current decelerator design. Thus, despite the factthat the Kr beam requires a higher phase angle for decel-eration (smaller decelerator acceptance) it results in moredecelerated molecules. After passing through the skimmer,the OH packet is spatially matched to the deceleratorentrance via an electrostatic hexapole. Details regardingthe OH Stark decelerator design and operating principlemay be found in previous work [27,28]. We utilize the142 stages of our Stark decelerator to slow a 130 mKpacket (in the comoving frame) of OH to 20 m=s at a phaseangle �0 � 47:45� for coupling into the magnetoelectro-static trap (MET). Decelerated OH packets are detected vialaser-induced fluorescence (LIF) upon entering the MET,whose center lies 2.7 cm from the final pair of decelerator

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rods. The 282 nm pulsed laser beam is oriented along themutual longitudinal axis (z) of the decelerator and MET,and the resulting 313 nm LIF is collected in a solid angle of0.016 sr.

The MET is illustrated in Fig. 1, and consists of twocopper coils operated in an anti-Helmholtz configurationsurrounded by an electric quadrupole. The center-to-centermagnetic coil spacing is 1.5 cm, providing a field gradientof 6700 G=cm by passing 1500 A through the 4 turns ofeach water-cooled coil. A longitudinal trap depth of400 mK is achieved, while the electrodes surrounding thecoils allow the application of an E field to the trappedsample. The double- and single-rod electrodes that com-prise the electric quadrupole allow the application of twodistinct field configurations. A uniform bias electric field iscreated by grounding the single rods while oppositelycharging the opposing double rods to �3 kV. Alterna-tively, we generate a quadrupole E field by charging neigh-boring rods with opposite polarities of �9 kV. Shieldingby the MET coils reduces the interior E field by a factor of�5. Figure 2 depicts the quadrupole electric field super-imposed on the magnetic quadrupole field. OH has both anappreciable magnetic and electric dipole, and we can easilyalter the geometry of the trapping potential by applyingelectric fields of variable magnitude and direction to themagnetically trapped sample.

The OH ground state is best described by Hund’s case(a), in which the spin (j�j � 1

2 ) and orbital (j�j � 1)angular momenta are strongly coupled to the molecularaxis, yielding the total angular momentum projectionj�j � 3

2 . The j�j � 12 state lies 126 cm�1 above this

ground state. The nuclear spin of the hydrogen atom (I �12 ) leads to a hyperfine splitting of the ground state into F �

2; 1 components. In the presence of large external fields(E> 1 kV=cm or B> 100 G), the electron angular mo-mentum and nuclear spin decouple [5], and one considersthe total angular momentum J, which includes nuclear andelectronic orbital angular momentum as well as electronspin. The projections mJ of J are defined along the axis ofthe applied field. The ground state is further split into twoopposite-parity states (f=e) by the coupling of electronicorbital angular momentum to nuclear rotation. This small�-doublet splitting of 1.67 GHz, along with the 1.67 Delectric dipole, is responsible for the rather large Stark shiftexperienced by OH molecules [29]. Figures 2(a) and 2(b)show the Zeeman and Stark effects of the OH ground state,respectively. External electric fields can thus dramaticallyalter the potential confining the magnetically trappedmolecules. Figures 2(c)–2(e) illustrate the field geometrieswithin the MET. In the plane perpendicular to z, Fig. 2(c)shows the radial B field characteristic of a magnetic quad-rupole, while Fig. 2(d) depicts the electric quadrupole fieldintroduced by the electrode geometry. Figure 2(e) illus-trates both B (small arrows) and E (large arrows) fieldsviewed from the side.

The top potential surface of Fig. 2(f) represents theenergy shift of the decelerated jJ � 3

2 ; mJ �32i state (E

FIG. 1 (color online). Illustration of the magnetoelectrostatictrap (MET) assembly. The terminus of the Stark decelerator,shown to the left, couples state-selected cold molecules into themagnetic quadrupole (a pair of rings in the middle). The double-electrode structure within the electric quadrupole (6 rods sur-rounding the magnetic quadrupole) allows for application ofuniform electric fields within the magnetic trap. The ring atthe back supports a 1 in. lens for collection of laser-inducedfluorescence.

FIG. 2 (color online). (a) Zeeman and (b) Stark effects of theground state structure of OH. (c) Magnetic and (d) electricquadruple fields viewed from z. (e) Side view of the METconfiguration with quadrupole E and B fields. (f) Transverseadiabatic potential surfaces for various components of the OHground state at the longitudinal MET center. The top surfacedepicts the decelerated and trapped jJ � 3

2 ; mJ �32i state.

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fields couple e and f, therefore they are no longer goodquantum numbers) within the combined quadrupole E andB fields present in the MET. The transverse profiles ofthe four trapping adiabatic potentials are depicted atthe longitudinal trap center, where ~B � z � 0. The remain-ing four surfaces (not shown) are simply inverted relativeto those displayed, and are therefore antitrapping. Thethree-dimensional MET potentials are calculated bydiagonalizing an effective Hamiltonian that includes bothStark and Zeeman terms. Coupling between the groundjJ � 3

2 ;� �32i and excited j 5

2 ;32i, j

12 ;

12i, j

32 ;

12i states is

included, for a total of 64 hyperfine components. ThejJ � 3

2 ;� �32i, j

32 ;

12i coupling is the most critical, increas-

ing the trap depth of the top surface of Fig. 2(f) by 11%.Addition of the remaining states modifies the potential by<0:1%. The square shape of the top surface is a result ofthe varying angle between E and B in the MET. Thepotentials from each field directly sum where the fieldsare collinear, but the trap shallows from this maximumvalue as the angle between E and B increases.

The Stark decelerator slows only those OH molecules inthe electrically weak-field seeking (EWFS) component ofthe ground state, i.e., the upper � doublet. Of these EWFSmolecules, only those with components J � 3

2 , mJ � �32

are synchronously slowed to 20 m=s. Because the positivemJ state is magnetically weak-field seeking, only 50% ofthe decelerated molecular packet is trapable by the MET.The molecules experience a B field >100 G at the lastdeceleration stage emanating from the back coil, preserv-ing the quantization of the decelerated state.

To trap the incoming OH packet, the coil closer to thedecelerator (front coil) is grounded while the coil furtherfrom the decelerator (back coil) operates at 2000 A for theduration of the 3.7 ms deceleration sequence. The effectivemagnetic dipole of OH in its J � mJ �

32 state is 1:2�B ’

0:81 K=T, where �B is the Bohr magneton, allowing theback coil to stop molecules with velocity �22 m=s. Thefront coil is turned on after the 20 m=s molecules arestopped by the back coil, which occurs 2.65 ms afterexiting the final deceleration stage. The trap switching issynchronous to the 20 m=s molecules since OH possessinglarger longitudinal velocities escape the quadrupole field.For technical reasons, the two magnet coils are connectedin series, causing the current in both coils to decrease from2000 to 1500 A over �800 �s once the front coil isswitched into the circuit.

Figure 3 displays typical time-of-flight data resultingfrom the trapping sequence along with results fromMonte Carlo simulation of the trap dynamics. The largeinitial peak is the decelerated OH packet traversing thecenter of the trap. All subsequent peaks are the result ofoscillation in the � dimension, with a frequency of�650 Hz. Fluorescence is gathered in �, and oscillationsin z are not detectable since our detection region spans theentire visible trap length. The magnetic quadrupole trap isunable to confine all the molecules stopped by the back coil

alone due to the 25% current drop, as is clear from thedifference in signal height at �2:5 ms versus the steady-state level at, e.g., 10 ms. Note the larger steady-statepopulation of Fig. 3(b) from the addition of a confiningtransverse electric quadrupole. Also visible is the shortercoherence time compared to Fig. 3(a), which results fromtrap distortion visible in Fig. 2(f). An estimate of the trapdensity, as measured by LIF, gives �3� 103 cm�3. Bycomparison, the density of a packet ‘‘bunched’’ at a phaseangle of �0 � 0� is 107 cm�3, while the 20 m=s packet is104 cm�3 due to its spreading during free-flight to the trapcenter. Previous work with electrostatic traps yielded�103

higher densities of trapped OH [15]. The trap density canbe further increased by decreasing the distance betweendecelerator and MET or by applying larger voltages to theelectric quadrupole. Monte Carlo analysis of the velocitydistribution of the trapped OH yields temperatures of�30 mK.

Higher decelerator phase angles should, in principle,produce a slower OH packet. However, below 20 m=s theOH population drops sharply and no further deceleration isobserved. We attribute this effect to a reduction in theeffective aperture seen by slow molecules as they traversethe final deceleration stage. The OH closest to the finaldecelerator rods see a larger longitudinal potential thanthose on axis and, at sufficient phase angles, are stopped or

a)

b)

LIF

sig

nal [

a.u.

]

0 2 4 6 8 10 12

200

150

100

50

0

Time from decelerator exit [ms]

LIF

sig

nal [

a.u.

]

0 2 4 6 8 10 12

200

150

100

50

0

Time from decelerator exit [ms]

FIG. 3 (color online). Time-of-flight data and Monte Carlosimulation results (solid red line) for two different MET con-figurations. The magnetic field switches from the stopping con-figuration to quadrupole trapping at t � 2:65 ms. (a) Magnetictrap only. (b) Stopping and trapping in the presence of combinedelectric and magnetic quadrupole fields. Note the larger steady-state trap population and damped oscillations compared to thezero E-field case (dashed gray line).

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reflected and hence cannot be observed in the MET region.Numerical models elucidate this effect, which may bemitigated by new decelerator designs [30].

The 10 Hz repetition rate of our Stark decelerator cur-rently limits our trap interrogation time to 100 ms. Main-taining continuous currents of 1500 A presents technicalchallenges due to heating in both the switching transistorsand cabling, which require water cooling. Figure 4 showselectric field-free OH trap lifetimes measured in two dif-ferent background pressure regimes: 1� 10�6 and 4�10�8 Torr, both dominated by N2 at 295 K. Nonidealpower supply control causes the trap current to decreasefrom 1500 to 1160 A at a rate of 2000 A=s. This lowers thetrap depth, resulting in a loss of 12� 2 s�1. After account-ing for this loss mechanism, we find background collision-limited lifetimes of 20� 5 and 500� 130 ms for the twopressure regimes, respectively. These lifetimes determinean OH-N2 collision cross section of 500� 100 �A2. Fromthis clear dependence of trap lifetime on background gaspressure, we envision measuring dipole-dipole collisioncross sections by using another beam of polar moleculescolliding under the E field of the MET.

We have magnetically confined ground state hydroxylradicals in a MET that allows for the application of a vari-able E field to the trapped polar molecules. Diagonal-ization of an effective Hamiltonian modeling the energyshift of OH in combined E and B fields was necessary foraccurate Monte Carlo simulation of the trap dynamics.Future experiments could quantify temperature dependentnonadiabatic transition rates between the different surfacesdepicted in Fig. 2(f) akin to Majorana transitions observedin atomic magnetic quadrupole traps. Furthermore, higherdensities within the MET will facilitate the study of coldOH-OH collisions in variable electric fields. As rather

modest electric fields are expected to modify collisioncross sections between polar molecules by as much as103 [17], crossed-beam experiments exploiting the METdescribed here will benefit from both low center-of-masscollision energies and tunable E fields in the interactionregion.

We thank DOE, NIST, and NSF for support, andP. Beckingham, H. Green, and E. Meyer for technicalassistance. B. L. thanks the NRC for financial support.

*sawyerbc@colorado.edu†Present address: Department of Physics, Yale University,New Haven, CT 06520, USA.

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FIG. 4 (color online). Measured (�) and deconvolved colli-sional (�c) lifetimes of magnetically trapped OH at a backgroundpressure of 1� 10�6 Torr (�) and 4� 10�8 Torr ().

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